Semidilute solutions screening effects

On the other hand, the crossover from dilute to semidilute regime in solutions of randomly branched polymers is strongly affected by size and shape polydispersity. In particular, at moderate concentrations, large dusters are overlapped, whereas the smaller ones still behave as in the dilute regime, penetrate the larger ones, and contribute to screening of the intramolecular exduded-volume repulsions. The concentration effects in semidilute solutions of polydisperse randomly branched polymers were analyzed in detail in Reference 158. 

The effect of added salt on the conformation of polyelectrolyte chains in dilute and semidilute solutions was investigated by Stevens and Plimpton [151], At high salt concentrations the electrostatic interactions between charged monomers are screened and the chain conformations are similar to those observed for good solvent, R As the salt concentration... 

Assume that we are dealing with polymers in good solvents and in the semidilute solution. If r is a scale to measure, then the chain entanglement shows the following properties. At r >, that is, outside the blob, the repulsive interactions between monomers are screened out by other chains in the solution so that the whole chain is composed of blobs connected in an ordinary random walk without excluded volume effect. Overall, the chain follows Gaussian statistics. At r <, that is, within the blob, the chain does not interact with other chains, but there is a strong excluded volume effect. 

Hence, no forces arise and the polymer chain does not expand. In the literature one often finds a particular formulation for addressing this effect. As the concentration gradient given for an isolated chain is compensated for by the presence of monomers from the other chains, one says that the latter ones screen the intramolecular excluded volume interactions. Here we leave it at this short remark. Further comments on this picture and the origin of the saying will follow at a later stage when we discuss the properties of semidilute solutions. 

Our considerations qualitatively explain the results of Fig. 3.16 The dissolution of salt in addition to the polyelectrolyte suppresses the osmotic pressure contribution by the counter-ions and transforms the stiffened polyelectrol3de chain into a much more flexible quasi-neutral chain. In the absence of these polyelectrolyte characteristics, one recovers the behavior of neutral systems and, therefore, in the semidilute range the associated scaling law Eq. (3.41). Equation (3.136) correctly describes the general tendencies, but is not an accurate expression. First, in view of the complex structures in polyelectrolytes with shell formations and screening effects, equilibria have to be expressed in terms of activities rather than concentrations. Furthermore, the Donnan expression is not the only contribution to the second virial coefficient. There exists another part, AA2, which accounts as usually for excluded volume effects, the quality of the solvent and the peculiar ordering phenomena found in polyelectrolyte solutions. Therefore, in general, one has to write... 

At length scales larger than the electrostatic interactions are screened by the other chains and counterions and the statistics of a chain is Gaussian with effective bond lengths of the order of the correlation length Thus, the chain size R in the semidilute salt-free polyelectrolyte solution is R - A /2c->/4 [26,29],... 

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